Uncertain discrete systems: Stability, instability, and an attractor

Autor: I. E. Zuber, A. Kh. Gelig
Rok vydání: 2015
Předmět:
Zdroj: Vestnik St. Petersburg University: Mathematics. 48:61-65
ISSN: 1934-7855
1063-4541
DOI: 10.3103/s1063454115020132
Popis: The system xk + 1 = A(k)xk is considered, where A(k) є ℝn × ℝn is a matrix coefficients aij(k) of which are nonanticipating functionals of any nature. It is assumed that the elements of the first to (p + 1)st columns above the main diagonal and the elements of the (p + 1)st to (n–1)st columns below the main diagonal satisfy the condition \(\mathop {\sup }\limits_k |{a_{ij}}(k)| \leqslant a.\) For the other elements, the estimate \(\mathop {\sup }\limits_k |{a_{ij}}(k)| \leqslant \delta \) holds. An upper bound for the values of the parameter δ at which system (1) is globally exponentially stable if \(\mathop {\sup }\limits_k |{a_{ii}}(k)| 1\) is obtained. In the case where the elements on the main diagonal are functions of xk and satisfy the conditions \(\mathop {\sup }\limits_{|{x_k}| > R} |{a_{ii}}({k_|})| 1\)\(|(i \in \overline {1,n} )\) for 0 < r< R, system (1) has a global attractor.
Databáze: OpenAIRE
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